Even if an organization were to attempt to rank classics PhD programs, it would be a useless list for most.
Classics has some very specific specialties which certain schools are well-known for being the best in, while otherwise not so strong. For example, the University if Cincinnati is probably the best for Bronze Age archaeology, but for every other aspect of classics it is mediocre. So how do you rank UCinn? This is the problem.
The bottom line is quite clear. For job security you need a PhD from an Ivy or the few 'Par-Ivies'. If you don't have a PhD from one of them you're pretty much out of luck. Unless of course you are a Bronze Age archaeologist with a PhD from UCinn, or another such 'exception school'.
Also, since there is only around 12 solid programs out there worth your time, what does it really matter to rank them? Apply to them all, whoever accepts you compare them. If you're accepted into even two top-12 programs you're a real fortunate applicant, so at that time worry about who is better by directly comparing the faculty, program, placement, fit, etc,...
But, if you asked for my simple, humble opinion of a general guide to a ranking of PhD classics programs... here you go.
1. Princeton University
2. UC-Berkeley (AHMA)
3. Stanford
4. University of Pennsylvania
5. Yale University
6. UNC-Chapel Hill
7. Columbia University
8. University of Michigan
9. University of Chicago
10. Cornell University
11. Brown University / Duke University
12. Harvard University
Yes, Harvard is 12th of the top-12. Take a good hard look at their faculty list; it is awful!! There is nobody there of any real significance--long gone are the days of Badian and Bowersock. Harvard is coasting in neutral right now, and quite honestly has been for the last 5-10 years. But it's Harvard. So the name is deliciously tempting to anyone who would get accepted, but from people that I know who are there, they all wished they chose somewhere else.
But....this is only "my" perception of the best schools. Now, to clarify, if I were to assign numerical values to these programs, Princeton would be a 100, and Brown/Duke would be about a 95. So no real heavy variation in the overall quality..... Harvard, probably dips to about a 90, with name recognition, job placement, and their amazing library being their saving grace.
How does Ohio State, UTexas-Austin, UCLA, NYU, Boston U, U-Cinn, CUNY, UVirginia fare? I would say in the low 70s. Maybe some people get jobs, but unless community college or private prep school is your goal stick to the top 12.